Sony has confirmed that name changes are indeed coming to PlayStation, allowing people to change their PlayStation Network usernames. A beta test is set for the near future, concluding at the end of November.
To be honest, though, this sounds like it's been a complex feature for Sony to implement. In the official press release, it writes: "This feature is compatible with PS4 games originally published after 1st April, 2018, and a large majority of the most-played PS4 games that were released before this date. However, please note not all games and applications for PS4, PS3 and PS Vita systems are guaranteed to support the online ID change, and users may occasionally encounter issues or errors in certain games." You'll be able to revert your username if you do face any bugs.
What's more, additional username changes won't be free. During the aforementioned beta, you'll be able to change your name as many times as you like, but only the first change won't cost you anything. After that, it's $9.99/£7.99 per alteration, although PlayStation Plus subscribers can do it for just $4.99/£3.99. You do all of this via your profile page.
PSN name changes are currently set to roll out in "early 2019". Sony says more updates are incoming.